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If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook. Title: The Gyroscopic Compass Author: T. W. Chalmers Release Date: May 22, 2018 [EBook #57200] Language: English *** START OF THIS PROJECT GUTENBERG EBOOK THE GYROSCOPIC COMPASS *** Produced by deaurider, Charlie Howard, and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive) THE ENGINEER SERIES T H E G Y R O S C O P I C C O M P A S S A NON-MATHEMATICAL TREATMENT THE ENGINEER SERIES THE GYROSCOPIC COMPASS A NON-MATHEMATICAL TREATMENT BY T. W. CHALMERS, B.S C ., A.M.I.M ECH .E. (O N T HE E DIT ORIAL S TAFF OF “T HE E NGINEER ” ) ILLUSTRATED L O N D O N CONSTABLE & COMPANY, LTD. 10 ORANGE STREET, LEICESTER SQUARE. W.C. 1920 Printed in Great Britain PREFACE T HE chapters composing this book originally appeared as a series of articles in The Engineer during January, February, and March of the current year. The articles were written in the belief that many readers would welcome a clear and full, non-mathematical exposition of the gyroscopic compass, its theory and practical construction. The gyro-compass represents at once the most involved and abstruse and the most important and valuable of all the practical applications to which the gyroscope, so far, has been put. As a navigational instrument it is now in practically universal use in all the chief war navies of the world, and is to-day being adopted by several important representatives of the mercantile marine. Remarkable figures were shown to the author recently which demonstrated that not only was navigation by the gyro- compass much more accurate than by the magnetic compass, but that the increased accuracy reduced the length of the voyage of a mercantile vessel to an extent that resulted in saving a quantity of fuel the value of which on a single trip would go a considerable way towards meeting the extra first cost of the gyro- compass. Bearing these facts in mind the author from the outset endeavoured not only to dispense with mathematics but to avoid introducing anything except the most familiar physical principles and conceptions, for his object was to explain the mode of action of the gyro-compass for the benefit primarily of the navigating officer—naval and mercantile. If some readers should find the treatment in places unduly prolix, the author trusts they will exercise leniency and regard the fault as being caused by the author’s unwillingness to take any risks in expounding a subject, no part of which can be understood incompletely without grave hurt to the understanding of the whole. T. W. C. L ONDON , May, 1920 CONTENTS CHAP. PAGE I. I NTRODUCTION 1 II. E LEMENTARY G YROSCOPIC P HENOMENA 4 III. T HE G YROSCOPE AND THE R OTATION OF THE E ARTH 15 IV D AMPING THE V IBRATIONS OF THE G YRO -C OMPASS 29 V T HE D AMPING S YSTEM OF THE A NSCHÜTZ (1910) C OMPASS 42 VI. T HE D AMPING S YSTEM OF THE S PERRY C OMPASS 52 VII. T HE D AMPING S YSTEM OF THE B ROWN C OMPASS 59 VIII. T HE L ATITUDE E RROR 65 IX. T HE N ORTH S TEAMING E RROR 71 X. T HE B ALLISTIC D EFLECTION 81 XI. T HE Q UADRANTAL E RROR 91 XII. T HE E LIMINATION OF THE Q UADRANTAL E RROR 107 XIII. C ENTRIFUGAL F ORCES DURING Q UADRANTAL R OLLING 130 XIV T HE A NSCHÜTZ (1910) C OMPASS 138 XV T HE S PERRY C OMPASS 142 XVI. T HE B ROWN C OMPASS 148 XVII. T HE A NSCHÜTZ (1912) C OMPASS 154 I NDEX 165 LIST OF ILLUSTRATIONS FIG. PAGE 1. Model gyroscope with three degrees of freedom 4 2. Model gyroscope with three degrees of freedom 7 3. Model gyroscope, frictional transmission of turning moment 9 4. Model gyroscope, one degree of freedom lost 11 5. Model gyroscope, second degree of freedom lost 12 6. Model gyroscope, lost degrees of freedom restored 13 7. Elementary gyroscope at equator 15 8. Gyroscopic clock 16 9. Elementary gyro-compass 18 10. Elementary compass at equator 20 11. Elementary compass at 55 deg. N. Lat. 24 12. Compass at equator and near North Pole 26 13. Pendulum and compass 32 14. Damped and undamped vibrations 35 15. Damped pendulum 37 16. Air-blast damping system of Anschütz (1910) compass 43 17. Free and damped motion of axle 49 18. Damping curve from Anschütz (1910) compass 50 19. Damping system of Sperry compass 53 20. Action of excentric pin in Sperry compass 55 21. Action of excentric pin in Sperry compass 57 22. Gyro-pendulum with axle tilted 60 23. Damping system of Brown compass 62 24. The north steaming error at 0 deg. and 60 deg. N. 72 25. Sperry correction mechanism for latitude and north steaming errors 76 26. Ballistic force on compass when ship’s speed changes 83 27. Ballistic force on compass when ship’s speed changes 84 28. Ballistic deflection 86 29. Effect of rolling on due north course 93 30. Effect of rolling on due west course 94 31. External gimbal mounting 97 32. Effect of rolling on a due north course (simple mounting) 98 33. Effect of rolling on a due north course (external gimbal mounting) 99 34. Ship rolling on N.W. course 101 35. Sperry compass on N.W. course 108 36. Sperry ballistic gyro 111 37. Stabilised excentric pin (Sperry compass) 112 38. Diagram of Brown compass 113 39. Oil control bottles (Brown compass) 115 40. Brown compass on west course 117 41. Diagram of Anschütz (1912) compass 121 42. Plans of gyros (Anschütz compass) 122 43. Centrifugal forces on a pendulum 131 44. The Anschütz (1910) compass 139 45. The Sperry compass removed from binnacle 143 46. The Sperry compass 144 47. The Brown compass removed from binnacle 148 48. The Brown compass removed from binnacle 149 49. The Brown compass 150 50. Plan of Anschütz (1912) compass 155 51. Sectional elevation of Anschütz (1912) compass 159 THE GYROSCOPIC COMPASS: A NON-MATHEMATICAL TREATMENT CHAPTER I INTRODUCTION A T this date it is, or should be, unnecessary to open an account of the gyroscopic compass with a discussion of the defects of the ordinary magnetic compass. These defects are too well known to require mention. Recent advances in naval architecture, particularly in warship construction, and very especially the building of submarines, have resulted in the magnetic compass becoming less and less useful for accurate navigation, primarily because of the upsetting influence exercised upon it by masses of steel or iron in its neighbourhood. It may still serve, perhaps, for the surface navigation of submarines, but for submerged runs the use of a gyro-compass is all but essential. In warships the weight of the guns and turrets is now so heavy that the magnetic compass can hardly remain unaffected by them and is materially influenced when the guns are trained to different directions. The shells themselves as they are discharged are also said to be a cause of error in the reading of the magnetic compass, for they tend in most positions of the ship to drag the needle after them by magnetic attraction as they pass along the bore of the gun. The value of the gyro-compass is not, however, recognised only in the world’s war navies. It is becoming increasingly appreciated in the mercantile marine, and there can be but little doubt that the device will soon be extensively employed on passenger liners and merchantmen generally. In the following pages we attempt to give an account of the working of the gyro-compass and to describe the forms assumed by the device in practice—sufficiently fully to illustrate the theory without going into any great detail on the constructional side—and to do so without depending upon the reader’s possessing mathematical knowledge. It is to be remarked that it is much easier to treat the gyroscope and all its practical applications mathematically than non-mathematically, and that the avoidance of mathematics generally leads to a discussion of this essentially mathematical device which is unscientific, unsound, and of very little practical value. We trust that our account will be found to avoid these defects and that it will prove useful and enlightening to those who have so far failed to understand the behaviour of the gyroscope and its applications by reason of the fact that hitherto all trustworthy descriptions have been couched in a highly mathematical form or have been mere mathematics thinly disguised in written words. It is admittedly not easy to understand gyroscopic phenomena either with or without the aid of mathematics, but on the other hand many of the difficulties of the subject are largely artificial. Thus the mathematician, when dealing with it, seems to be much more concerned with his equations than in creating a mental picture of what they represent; yet every one of his equations can be or should be capable of being represented physically. Those who set out to avoid mathematics do not usually succeed in giving a discussion sufficiently complete to be of any practical service afterwards to their readers. Thus in dealing with the gyro-compass the so-called “popular” description in most cases begins and ends with an explanation of why the device possesses directive force when it is set up at the equator. It is quite easy to demonstrate the existence of such force at the equator. It is not so easy to show non-mathematically how the directive force is generated and applied when the compass is situated north or south of the equator. The necessity for damping the horizontal vibrations of the gyro-axle and how the required damping force is applied in practice are still more difficult to explain, while the errors to which the gyro-compass is open—such as the latitude and the quadrantal errors—are even more trying to make clear. The latter subjects are usually neglected in the “popular” account of the compass. Yet without some means of damping the vibrations referred to or of eliminating or allowing for the various errors, the compass, even though it can be shown to possess directive force in all latitudes, would be utterly useless—especially on board ship—as a direction indicator. Finally, it may be remarked that while the gyro-compass represents to-day probably the most intricate and involved practical application of the gyroscope, it is not the only one of importance. This fact is to our advantage, for if we succeed in explaining the theory and working of the gyro-compass we shall have succeeded in placing the reader in a position enabling him readily to understand all other devices in which a gyroscope is employed or in which gyroscopic phenomena are developed. CHAPTER II ELEMENTARY GYROSCOPIC PHENOMENA L ET a wheel A (Fig. 1) be mounted on an axle B C journalled within a horizontal ring D. Let this ring in turn be mounted on journals E F within a vertical ring G and, further, let this vertical ring be carried on journals H J within a vertical frame K. This arrangement constitutes a gyroscopic system having three degrees of freedom, because relatively to the frame K the wheel may turn about three axes B C, E F, and H J mutually at right angles to each other and because, if the wheel is set spinning on its axle, gyroscopic properties will be manifested. F IG . 1. Model Gyroscope, with Three Degrees of Freedom. The following is a brief statement of the gyroscopic properties manifested when the wheel is spun on its axle: ( a ) Let the wheel be spinning in the direction of the arrow L and let a weight W be hung on the horizontal ring at the end B of the axle. The movement produced by this weight is not a rotation of the horizontal ring, and the wheel within it, about the axis E F. Instead, the horizontal ring remains horizontal and the whole system inside the square frame sets off rotating at a uniform speed about the axis H J in the direction of the arrow marked M on the horizontal ring. This rotation or precession, as it is called, will be maintained so long as the weight W remains in action. There is here no question of perpetual motion. The work expended in overcoming the friction at the vertical journals is derived from the energy of the spinning wheel, and when this energy is exhausted the phenomenon ceases. The phenomenon can, in fact, only be maintained indefinitely by expending power to drive the wheel against the leakage of energy through friction at the journals of the axle and the vertical axis H J. A closer examination of the phenomenon would show that there is a slight rocking motion of the horizontal ring on its axis E F, and therefore an additional leakage of energy at the journals of this axis. This rocking motion can be neglected for our present purposes. It is sufficiently accurate to say that the horizontal ring remains horizontal. ( b ) The speed of the precession is proportional to the weight W and to the speed of rotation of the wheel on its axle. For instance, doubling the weight doubles the speed of precession. ( c ) If the direction of spin of the wheel is reversed the direction of the precession is also reversed. ( d ) If the spin of the wheel is in the direction L, and if instead of attaching a weight at the end B of the axle we exert an upward force at this point the precession developed will be opposed to the direction of the arrow M. ( e ) If instead of trying to rotate the wheel about the axis E F by means of a weight or force applied at B we attempt to turn it about the vertical axis H J by applying a horizontal force V to the outer ring, the wheel will not turn about the vertical axis H J, but about the horizontal axis E F, the end B of the axle rising up towards H. ( f ) As before, the direction of this movement is reversed by reversing either the direction of spin of the wheel or action of the force V . If both are reversed simultaneously the direction of the movement produced by the applied force is not altered. The behaviour set forth above can be summarised in a general rule as follows:—If to a spinning wheel possessing three degrees of freedom a force be applied tending to turn the wheel about some axis X X, the actual motion produced will not be about X X but about some other axis Y Y; this axis Y Y will be such that rotation about it will tend to bring the axle of the spinning wheel into coincidence with or parallel with the axis X X; the direction of the rotation produced about Y Y will be such that when the condition of coincidence or parallelism is reached the spin of the wheel will coincide in direction with the rotation we are attempting to produce about the axis X X. Taking case ( a ) (Fig. 1), it will be seen that the axis E F about which we are attempting to produce rotation by means of the weight W, together with the weight W itself, is of necessity carried round by the precession in the direction M at the same rate as the axle of the spinning wheel. The axle in this case cannot therefore place itself in coincidence with the axis of the applied force. But it does its best to do so. The precession persists and is an expression of the fruitless chase of the axis E F by the axle B C. F IG . 2. Model Gyroscope, with Three Degrees of Freedom. If, however, the weight is attached by some kind of sliding connection on the horizontal ring in such a way that its line of action remains stationary in space, then the axis about which we are attempting to produce rotation will also remain stationary in the position occupied by the axis E F before precession commences. In this case it is quite possible for the axle of the wheel to place itself in coincidence with the axis of the applied force. Precession about H J through 90 deg. will accomplish this result, as indicated in Fig. 2. The weight W is now acting at a point on the horizontal ring where it ceases to have any tendency to turn the wheel about the axis E F. When, therefore, the position of coincidence is reached precession ceases and the system comes to rest in this position. If the experiment were actually made it would be found that the momentum acquired by the system during the 90 deg. turn would carry the axle through the position of coincidence with the axis of the applied force. But immediately the axle passes to the opposite side the force W is exerted on a point of the horizontal ring between F and C. The action of the force passing on to this, the opposite, segment of the ring reverses the conditions under which the system started its movement and as a result precession in the direction opposed to the arrow M is set up. The axle thus tends to recover its position of coincidence and in the end settles down to a vibratory motion from side to side of the axis of the applied weight. Friction at the vertical journals will “damp” this vibratory motion, the amplitudes of the swings will decrease, and the axle will ultimately settle in steady coincidence with the axis of the applied force. In this condition the force will have no further effect on the system beyond throwing a bending moment on to the vertical axis. F IG . 3. Frictional Transmission of Turning Moment. Instead of trying to make the wheel rotate about the axis E F by applying a weight to the inner ring as in Fig. 1, let us, as shown in Fig. 3, mount the square frame K on a horizontal axis N P and attach the weight W to an arm fixed on the frame. The axes N P and E F being—at least initially—collinear, the effect of this arrangement is to throw a turning moment on to the wheel about the axis E F just as does the weight W in Fig. 1. It is to be noticed, however, that the moment of the weight W in Fig. 3 about the axis N P is transmitted to the inner ring as a moment about the axis E F solely because of the friction existing at the journals of the axis E F. This friction may be very small, so that the turning moment received by the wheel is only a very small fraction of the turning moment exerted by the weight W about N P. The effect of the arrangement is thus exactly the same as would be produced in the arrangement Fig. 1 if we reduced the weight W to a hundredth or a thousandth of its value. In other words, precession about the vertical axis H J will set in in the direction of the arrow M just as before, but the speed of this precession will be only a hundredth or a thousandth of the previous value. It is not very important to trace out the behaviour of the system shown in Fig. 3 beyond a very brief period immediately after the weight W is applied. The point of importance is that the precession produced by the weight is very slow, and therefore that in a given interval of time the amount precessed is very small. Further, the rate of the precession depends solely upon the friction at the journals of the axis E F and not upon the weight W or the movement of the frame K except in so far as these factors affect the friction. The less the friction the less will be the rate of precession and the amount precessed in a given time. Thus by mounting the axis E F on knife edges the friction can be made so small that the precession produced by the weight W becomes immeasurable. Hence we deduce that if friction is substantially absent at the axis E F the frame K might be violently rocked on the axis N P or even set into continuous rotation without causing the axle of the wheel either to dip or to precess. Continuing the argument, we might mount the square frame on a vertical axis and attempt to produce rotation of the wheel about the axis H J by applying a horizontal force to one side of the square frame instead of a force V on the outer ring as shown in Fig. 1. A similar result would be obtained. Granted an all but total absence of friction at the journals of the vertical axis H J, the precession produced about the horizontal axis E F would be immeasurably small. Thus the frame might be set into violent motion about its vertical axis without causing the axle either to rotate in a horizontal plane or to precess in a vertical one. F IG . 4. One Degree of Freedom Lost. Finally, if the square frame were mounted on a horizontal axis collinear with the axle B C it might obviously be rotated about this axis without affecting the system otherwise than by increasing or reducing the rubbing speed of the axle B C in its bearings. Since pure translation of the frame in any direction cannot apply a turning moment to the system about any axis, and as rotation of the frame about any one of the three principal axes has no effect which is measurable on the orientation of the axle, it follows that, given substantial absence of friction at the axes E F and H J, the axle of the wheel will remain constantly pointing parallel with its original position, no matter how the frame K may be moved or turned about. F IG . 5. Second Degree of Freedom Lost. The gyroscopic system shown in Fig. 1 has, as we have said, “three degrees of freedom,” because its wheel is free to spin about three different axes mutually at right angles. It is to be carefully noted that it can only truly be said to have three degrees of freedom so long as the inner ring and the parts inside it are not rotated on the axis E F away from the position which in Fig. 1 they are shown as occupying relatively to the outer ring. Thus rotation of the wheel on its axle or of the whole system inside the square frame on the axis H J leaves the three axes B C, E F, H J undisturbed at right angles to each other. But rotation of the inner ring and the parts inside it on the axis E F tends to destroy one of the degrees of freedom. If, for instance, the inner ring is rotated through 90 deg., as shown in Fig. 4, the axle B C and the axis H J will coincide in direction. In this position the wheel cannot be rotated about a horizontal axis at right angles to E F and has therefore virtually only two degrees of freedom, namely, about the axis E F and about the axis H B C J. Again, if with the inner ring in the position shown in Fig. 4 the outer ring is turned through 90 deg. relatively to the square frame, the system assumes the configuration shown in Fig. 5 and the wheel loses the power of rotating about a horizontal axis in the plane of the square frame. F IG . 6. Lost Degrees of Freedom Restored. If, then, in any application of the gyroscope it is necessary to guarantee that the system shall have three degrees of freedom in all possible configurations, the simple mounting shown in Fig. 1 will not serve the purpose. It can be made to do so in the manner shown in Fig. 6, namely, by mounting the square frame inside a gimbal ring X, which in turn is supported by a frame Y, the two new axes T U and V W being at right angles to each other. In the position shown in Fig. 4 the new axis T U would restore the lost third degree of freedom, while the second new axis V W would restore the degree of freedom lost when the system assumed the configuration shown in Fig. 5. In the gyro-compass it is necessary to guarantee that the spinning wheel in all possible configurations shall have three degrees of freedom, and accordingly we find the wheel mounted in a manner reproducing the features of Fig. 6. On the other hand, the majority of the movements which the compass system is called upon to make do not entail anything except very small degrees of rotation of the inner ring and wheel about the axis E F (Fig. 1), and therefore for most purposes the simple mounting there shown reproduces the required three degrees of freedom sufficiently closely to permit us to use it for demonstration purposes. In one very important portion of our subsequent discussion, however—namely, that dealing with the effect on a marine gyro-compass produced by rolling and pitching of the vessel—it will be necessary for us to take cognisance of the fact that the square frame shown in Fig. 1 is not fixed directly to the ship’s deck, but is really carried in gimbals as shown in Fig. 6.